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Standard Form
Concept of Significant figures 1. Significant figures '''refer to the digits of a number that is relavent to its precision. 2. The greater the number of significant figures, the greater the degree of accuracy. 3. Thus, the digits that are significant in a number are called the significant figures. The most significant figure is the left-most digit that is not a zero. 4. The most significant figure of a number is called the '''first significant figure. The significant figures after the first significant figure are called the second significant figure, third significant figure and so on. 5. For a decimal, all digits after the first significant figure are significant figures. 6. In rounding off '''positive numbers to a given number of significant figures, the following rules must be followed strictly: (a) '''All non-zero digits '''are significant. (b) '''Zeros occuring between non-zero digits are significant. © In a decimal, all zeros before a non-zero digit are not significant. (d) In a decimal number, zeros after the non-zero digits are significant. The zeros on the right of a non-zero digit are used to show the degree of accuracy. So, they are significant figures. (e) If a whole number is already rounded off, the final zeros are not significant. Concept of Standard Form 1. A number written in the form, Ax10 (power "n"), where 1 < A < 10 and "n" is an interger, is said to be in standard form. Another term for standard form is scientific notation. 2. Standard form allows us to prevent large and small numbers in a form that is easy to read, write and understand. It also helps us to compare large numbers and small numbers more easily. 3. A number written in standard form is a product of two numbers: 3.9 = a number between one and ten, excluding ten itself. 10 (power "12") = a power of ten. 4. Three simple steps to write a number in standard form: Step 1: Form the given number, identify A, where 1 < A < 10. Step 2: Count the number of decimal places you need to shift from A in order to get back the original number. Step 3: If you have shifted "n" places to the right, write "n" as positive "n". If you have shifted "n" places to the left, write "n" as negative "n". 5. Problems in standard form are easily solved with the help of a scientific calculator. Before embarking on any claculations in standard form, always set the calculator to the mode for standard form, always set the calculator to the mode for standard form so as to automatically display the required answer. 6. To convert a number more than 10 '''in standard form to a single number, press "ENG" repeatedly till n = 0. 7. To '''convert a number less than 1 in standard form to a single number, press "SHIFT" "ENG" repeatedly till n = 0. 8. To convert a number in standard form to a single number without using a scientific calculator: (a) for a number which is greater than or equal to 10, we shift the decimal point to the right. (b) for a number less than 1, we shift the decimal point to the left. 9. It is advisable to use scientific calculator in solving problems in standard form due to speed and accuracy. 10. For multiplcation of numbers in standard form, the terms with base 10 have to be grouped together first. 11. For division of numbers in standard form, the terms with base 10 have to be grouped together first. Vocab Corner 1. significant figure - angka bereti 2. accuracy - kejituan 3. rounding off - membundarkan 4. standard form - bentuk piawai 5. compare - banding 6. automatically display - memaparkan secara automatik 7. single number - nombor tunggal